Simpson gave birth to her baby on Tuesday in a LA hospital. The baby weighed 9 pounds 13 ounces and she measured in at 21.75 inches.

Simpson and her fiance, Eric Johnson, named their baby Maxwell Drew Johnson, according to TMZ. The couple decided to use the name Drew because that is Simpson's mother's maiden name.

According to US Magazine, Jessica and the baby are both doing just fine. Simpson also wrote on her website that she was grateful for all of the support she has received.

According to MTV, its the first child for the couple. Johnson and Simpson has been engaged since November 2010.

Simpson does not plan on marrying Johnson until she has a svelte frame. She said that she wants Johnson to be her husband very badly, she said to Jay Leno. She also told Leno that she wanted to wait to get married until after she had the baby but now the baby will actually be in the wedding.